You can not navigate the XMB without a Paired device (controller, remote). If you don't have a controller, and the remote is not Paired, you are out of luck.
Find someone with a PS3 and ask to use their controller, once the remote is Paired, you can give the controller back.
You can also go and see if you can find a used PS3 controller for cheap, so you don't have to spend the money on a brand new one (you might even be able to find a SixAxis only controller for cheaper than a DualShock 3).